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OCR for page 296
Breaking waves generated by a fast displacement ship model
A. Olivieri, F. Pistani, A. Di Mascio and R. Penna.
INSEAN, (Italian ship model basin), Via di Vallerano 139, 00128 Roma.
ABSTRACT
Bow and shoulder wave-breaking, generated by a fast
displacement ship model (INSEAN model 2340) has
been experimentally investigated. Both the mean and
the rms point wise values of the wave height have been
obtained by means of a finger probe. The intensity of
the breaking is highlighted by the highest values of the
wave fluctuations nearby the bow wave crest. The
velocity field under the free surface was measured 0.2
Lpp downstream the fore perpendicular by means of a
5-hole Pitot probe. These measurements were
performed just downstream the maximum of the wave
fluctuation. Very detailed database for CFD validation
was carried out for the wave height. The measured
velocity field completes the database and highlights
interesting flow features. Uncertainty assessment of the
wave height and velocity results was performed
following the AIAA Standards S-071-1995.
Preliminary CFD results from a RANSE code (without
a breaking model) are shown in comparison with the
measured data.
INTRODUCTION
Although wave-breaking phenomena are frequently
present in naval hydrodynamics applications, they are
far from being completely understood. From the
physical point of view, it is crucial to understand how
breaking waves are generated, and how they modify the
flow field. Furthermore, from the engineering point of
view, it is important to have a physical model in order
to take into account the effect of the wave-breaking.
Nonetheless, all models need a calibration that can be
performed only if experimental data are available.
Presently, available models for breaking wave
simulations are not able to describe the
three-dimensional case, while, they well reproduce 2D
classical experimental results [2], (see e. g. t33~.
Colagrossi et al. [4] recently proposed a
"2D+tmeshless model " in order to simulate breaking
waves around a ship, obtaining results that qualitatively
represent the breaking scenario.
Intensive experimental works have been carried out in
order to obtain experimental data on ships breaking
waves. Dong et al. provide a very complete and useful
database for the case of the DTMB 4817 model, in
terms of mean and instantaneous cross-flow by PIV
system [51.
A critical point in wave breaking experiments being the
effect of the surface tension, which can determine
formation of capillary waves, it is necessary to obtain
experimental results independent of it. In fact, surface
tension is a physical characteristic of the water used in
the experiments and it changes in different
experimental realizations. Furthermore is not easy to
measure the surface tension in order to quantify its
effect on breaking. The presence of surfactants is not
avoidable in large basins, so surface tension can change
even during the same experiment. The influence of
capillary waves on the wave breaking process is
increasingly important for smaller wavelength t6, 73.
Thus, it is necessary to perform experiments on large-
scale model flows and relatively high Froude number in
order to generate long waves. For these motivations, we
decided to perform measurements of the breaking wave
flow generated by a large model scale (Lpp = 5.72 m) at
relatively high Froude number (Fr = 0.35~.
The model INSEAN 2340 is an identical geosym of the
DTMB 5415 model that has been adopted by the
International Towing Tank (ITTC) as a recommended
benchmark for CFD validation for resistance and
propulsion (ITTC, 1996 [101~. A previous experimental
study, regarding far field wave elevation was performed
for Froude numbers Fr = 0.28 and Fr = 0.41 [13. In the
case of Fr = 0.28, the wave breaking was too gentle and
affected by capillary waves formation, while at
Fr = 0.41 the breaking was largely developed, plunges
and large spray formation was observed. The present
Froude number (Fr=0.35) has been selected on the
bases of a previous photographic study. We observed
that for Froude numbers larger than Fr = 0.325, the bow
wave breaks without appearance of capillary waves. On
the other hand at Froude number larger than Fr = 0.35,
the bow wave breaks producing large spray, which
makes the wave height measurement not practicable.
Preliminary results from numerical simulation using a
RANSE code have been reported. It has been noted the
tendency to develop a roll close to the surface even
without a model for the breaking waves.
OCR for page 297
MODEL GEOMETRY AND EXPERIMENT
DESIGN
The INSEAN model 2340 is an identical geosym of the
DTMB 5415 model, adopted by the International
Towing Tank Conference (ITTC) as a recommended
benchmark for CFD validation for resistance and
propulsion [101. It was conceived as a preliminary
design for a surface combatant. The model, whose lines
are shown in Fig. 1, presents a transom stern and a
bulbous bow of peculiar shape, designed for the sonar
lodging. Its length between the fore and aft
perpendiculars is Lpp = 5.72 m, which corresponds to a
scale ~ = 24.8. The main geometric parameters of the
model are given in Tab. 1. All tests have been
performed with the bare hull.
The model has been made of wood at the INSEAN
workshop. In order to stimulate turbulent flow, a row of
cylindrical studs of 3 mm height and 3 mm diameter
have been fitted on the model 0.05 Lpp downstream the
fore perpendicular, with 30 mm spacing.
The experiments have been performed at INSEAN
basin n. 2, which is 220 m long, 9 m wide and 3.5 m
deep.
During the tests, the model was held fixed, with trim
and sinkage set to the values previously determined in
unrestrained conditions t81. The nominal speed has
been set to U0 = 2.621 m/s, corresponding to Froude
number Fr = 0.35 and Reynolds number Re = l.sx107.
The wave height has been measured by a
servo-mechanic probe (Kenek SH), mounted on a
system of slides fixed to the carriage. The wave field
has been obtained measuring point by point along 81
transverse cuts from the bow to about midship. The
transverse displacements (2 cm) were actuated
automatically, while the longitudinal ones (4 cm) were
obtained manually. The acquisition time interval was
set to 2.2 s and the sample rate to 1000 Hz. The carriage
acceleration was lowered as much as possible in order
to reduce the wave fluctuations due to the transient
wave components (see for example [23~.
Velocity field has been measured on the port side, at a
x-station located 0.2 Lpp downstream the fore
perpendicular, using a 5-hole Pitot probe. A classical
Pitot tube has been used to measure the static pressure
in the undisturbed flow region, far enough from the
model. Five differential pressure transducers (Valydine
DP15) have been connected to the five Pitot holes and
to the static pressure hole of the Pitot tube t81.
The acquisition system run automatically, guided by
software implemented at INSEAN. Two orthogonal
slides, actuated by two step-motors, drove the Pitot to
the measuring point, starting from a reset position. The
two step-motors have a resolution of 200 steps per
revolution and the manoeuvring screw has a pitch of
10 mm, so that the spatial resolution of the device is
0.05 mm in vertical and transverse direction. The
carriage speed signal was checked by the software
before starting the acquisition and during the
acquisition itself. When the signal was within a
pre-defined range, the acquisition started. At the end of
the acquisition, the system moved the Pitot to the next
measuring point.
A regular grid with square cells, whose side dimensions
are ~ xg = ~ yg = 0.0025 Lpp, has been drawn just
below the free surface.
The adopted sample rate was fs= 100 Hz and the
acquisition time interval was set to la = 4.6 S.
depending on the distance from the free surface, in
according with a previous analysis performed to
determine the time needed to have a steady average.
The three-velocity components and the pressure
coefficient, in the measuring point, were calculated by
software through the calibration maps [8], with real
time preview.
In the following, the Cartesian frame of reference is
considered fixed to the hull, with the origin at the
intersection between the fore perpendicular and the
undisturbed water plane. In particular, x, y and z axes
are in the direction of the uniform flow, starboard side
of the hull and upward, respectively, and the
corresponding velocity components are ~ (axial), v
(transverse) and w (vertical).
Description
Fig. 1: test model INSEAN 2340
Scale factor ~
Length between perpendiculars LPP (m)
Draft
Displacement
Displaced Volume
Wetted surface area
142.0
B (m) 18.9
T (m) 6.16
(t) 8636.0
V (m3) 8425.4
Sw
(m2)
Hull coefficients
Lpp /B 7.530
B/T 3.09 1
_ ) 11.0
Ship Model
24.824
5.720
0.76
2949.5
0.248
0.549
0.549
4.786
CB V/( LppBT) 0.506
Cp V/( LppAx) 0.613
Cx AX/BT 0.825
Tab. 1: Geometrical data for INSEAN model 2340 and
full-scale ship.
2
OCR for page 298
WAVE-HEIGHT FIELD
A preliminary photographic study has been carried out
in order to set the Froude number. In particular, we
observed that, for low Froude numbers (<0.35), the
breaking occurs with appearance of capillary waves,
due to the relatively small wavelength of the divergent
waves. This occurs only for the ship model case, so that
the analysis on the wave pattern cannot be extended to
the full-scale case.
On the other hand, for relatively high Froude numbers
the breaking is characterized by the presence of spray,
which makes the wave height measurements not
practicable. As a satisfactory compromise between the
two requisites, the Froude number has been set to
Fr = 0.35. Photographs of the ship model bow-wave are
shown in figures 2- 8, for seven different Froude of
numbers, from Fr = 0.28 to Fr = 0.45. n 's
(transient) wave components and electronic noise.
Patterns of the mean and rms value of the wave
elevation are shown in figures 9 and 10. The highest
values of the rms indicate presence of fluctuations of
the wave elevation due to wave breaking. The bow
wave breaking is quite strong with the maximum of the
rms value of about 1/10 of the maximum wave height.
A typical trace of the acquired signal in the breaking
region is shown in figure 11. Although the shoulder
wave crest is under the undisturbed water level, it
manifests a gentle spilling wave breaking, as underlined
by the grey strip in figure 10. The shoulder wave
breaking is probably induced by the bow breaking
wave. In fact, in the farther field the shoulder wave
crest is positive and does not break [113.
Figs 2-4: bow breaking wave generated by the INSEAN
2340 model at Froude numbers smaller than Fr = 0.35;
1) Fr = 0.28, 2) Fr = 0.30, 3) Fr = 0.325.
Figs 5-7: bow breaking wave generated by the INSEAN
2340 model at Froude numbers larger than Fr = 0.35; 4)
Fr=0.375,5)Fr=0.41,6)Fr=0.45.
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
x
Fig 9: wave height contours (mean value)
-0.2,
-0.~S
-0.05
o
0.05
Fig 8: bow breaking wave generated by the INSEAN
2340 model at Froude number Fr = 0.35.
The wave height in the bow and shoulder region of the
near field wave pattern has been measured. The mean
value and the rms value have been carried out after
frequency analysis and filtering, which allowed to
reduce the error due to the presence of spurious
n nnF+nn 7 27F.11d ~17F Be Q Ills F.n~
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
X
Fig 10: wave height contours (rms value)
15
1O '
is
Fig 11: breaking and non-breaking wave height signal
time traces
3
OCR for page 299
VELOCITY FIELD INDUCED BY THE BOW
BREAKING WAVE
The velocity field has been measured on a cross-section
just downstream the bow wave front (x = 0.2~.
Measurements have been obtained by S-hole Pitot
probe. The adopted procedure is the one described in
[81. The results are shown in figures 12.15 in terms of
axial velocity contours and cross-flow vectors,
transverse velocity contours, vertical velocity contours
and axial vorticity.
n
.n n1
on,
-0.1 y -0.075
Fig 12: axial velocity contours and cross-flow vectors
at section x = 0.2; reference vector (top-right) is equal
to the nominal velocity U0 = 2.621 m/s, the mean value
of the wave height is shown by solid line + the rms
value (dashed lines).
-0.02
on',
.n no
Fig 15: axial vorticity contours at section x = 0.2, the
mean value of the wave height is shown by solid line +
the rms value (dashed lines).
The wake field generated by the bow breaking wave is
clearly shown by axial velocity and vorticity contours.
Although the maximum of the axial vorticity is inside
the wake, it is possible to recognize presence of vertical
flow, quite far from the wake. This is more clearly
shown in figure 16 where an offset value has been
subtracted to the cross flow velocity components.
According to this results, the picture in figure 17
displays the presence of vertical flow (rolls), quite far
from the hull and very close to the free surface.
o.o~
-0.125 -0.1 y -0.075 ADS
Fig 13: transverse velocity contours at section x = 0.2;
the mean value of the wave height is shown by solid
line + the rms value (dashed lines).
on' _
.02 _
. ...,... ..,, .. -- ~
I-....
1
. l
l
-1
Fig 14: vertical velocity contours at section x = 0.2; the
mean value of the wave height is shown by solid line +
the rms value (dashed lines).
on 25 ~.1
Fig 16: cross-flow associated to the rolls (obtained
subtracting an offset value to the transverse and vertical
velocity components); reference vector (top-right) is
equal to the nominal velocity U0 = 2.621 rn/s
Fig 17: vortices induced by wave-breaking
4
OCR for page 300
UNCERTAINTY ASSESSMENT OF THE
EXPERIMENTAL RESULTS
Uncertainty assessment of the results has been carried
out following the AIAA Standards S-071-1995, for both
wave elevation and velocity. Test measurement points
and related uncertainties are reported in table 2 and
table 3.
x _
0.07s
0.100
0.125
0.150
y
-0.09
-0.09
-0.09
-0.09
_
3.0010
3.91 10
s.20 10
9.07 10-
_
s.so 10-
5.81 10-
7.96 10-
8.53 104 _
Unc.
()
1.45 10
s
7.33 10
8.39 10
4
1.6110
Unc.
(ham)
9.5010
.12 10
.40 10
.9910
Tab. 2: Uncertainty assessment results for the wave
height
| Unc. (m/s)
| Unc. /U*
_
-0.3258
2.4551
0.9367
1.80 10-2
0.687 %
-0. 1243
_
8.9910-3
1.47 %
_
0.0595
0.0227
9.67 10-3
1.58%
Tab. 3: Uncertainty assessment results for the velocity
(y = - 0.1015, z = - 0.005); U* = Uo for the axial
velocity component, while, for transverse and vertical
components U* corresponds to their range of variation
in the measured field.
NUMERICAL RESULTS
The numerical simulation were performed by means of
a RANSE code for the simulation of free surface flows,
developed at INSEAN. Details of the algorithm and
computational examples can be found in (Di Mascio et
al., 2001 [123~. The one equation Spalart-Allmaras
model t13] was used to compute the eddy viscosity.
The flow was computed for the same condition as the
towing tank tests. The Froude number was set equal to
0.35 and the Reynolds number to 1.57x107. The
solution was computed with a grid made of 13 blocks,
for a total of about 1.6x106 cells. The computed wave
pattern is reported in figs.18 and 19, close to the bow
and the stern, respectively. The global wave pattern is
compared with the measured data in fig.20. As it can be
noticed, the computed wave height at the bow is higher
than the measurements. This is to be ascribed to the
lack of any model to simulate the rather strong breaking
wave observed in the experiments. The velocity field is
reported in fig.21, in terms of axial velocity and cross
flow vectors, in the cross sections x= 0.05, 0.10, 0.15
and 0.20. The wave profile in the yz plane can also be
observed. Again, the predicted profile is poorly
predicted in the breaking region, an probably also the
vertical flow caused by the overturning wave is not
well represented. Nonetheless, the predicted flow shows
the tendency to overturn close to the wave crest as in
the experimental data (figs 12, 16 and 20 x = 0.2~.
CONCLUDING REMARKS
The measurements were intended as a database for
CFD validation. In fact, the ship flow predictions
obtained by numerical codes in presence of 3D wave
breaking is quite difficult and needs many effort in
order to predict and follows the breaking waves.
Nonetheless, present experimental results give
important indication on the physics of the flow
generated by ship (model) breaking waves.
Measurements on two more cross sections, respectively
located at x = 0.15 (:just upstream the section
investigated in present work) and x = 0.4, have been
planned in order to better understand the rolls
generation at the bow breaking wave and the flow
resulting from the shoulder breaking wave. Moreover,
an extension of the investigated wave field has been
planned along the shoulder wave crest [111.
The numerical results, even if without any breaking
model, show the tendency of the flow to form
quasi-streamwise rolls, downstream the bow breaking
wave. The modeling of the breaking wave and the
production of turbulence and vorticity beneath the
breaking region is the subject of further research.
0.4
0.3 _
0.2
0.1
n
n 1~
0.1 .
D.08
0.06
0.04
0.02
s
. . :. i,,'~
~ ' .'....1 ... ;...1...1 J~ 1 i f~ 1 1 ~
-0.7 -0.6 -0.5 -0.4 -0.3
X
-0.2 -0.1
_ _ . ,j,.
,-
_ , .
,,...'
_
,,. //
~ ~ ~3 ~ ~ ~ ~
X
Figs 18,19: numerical wave field
OCR for page 301
0.02
On
-o.od
fain!
Pond
in n
0.02
0.01
1
nnA
-o os
.n of
.n no
0.03
0.02
0.01
o
-0.01
-0.02
-0.03
r.O,04
-0.05
-0.06
-0.07
-0.08
-0.0
Y—n 1
0.025 0.05 0075 0 1
y
0.02 t
nn1
o
-0.01
-0.02
~4
-0.03
Ant
.n no
-0.06
in n7
0.6
0.5
0.4
0.3
-0.1
-0.2
-0.3
-0.4
W...
. DTMB 5415
. Fr=0.35
Re = 1.575e+7
..
NU M ERICAL
_......................................................
. . . . . . . . . . . . .....
. ....
. ..~-.~ '2".--:''T,~' 6''"~ ', ~'"'~ " ;'' ' i
-0.4 -0.2 0 0.2 0.4 0.6
x
Fig 20: numerical vs experimental wave field
-
x=o.oe
x=O.1 0
. ,
1,. ....... ...........
0 0.025 0.05 0.075 0.1
y
Fig. 21: velocity field contours of the axial velocity component and cross flow vectors.
6
OCR for page 302
0.02 t
0.01 ~
Inns
-O.OZ
~4
-0.03
-0.04
nest
-0.06
-0.07,
0.03
0.02
0.01
o
-0.01
-0.02
-0.03
~0.04
-0.05
-0.06
-0.07
-0.08
-0.09
-0.1
x=0.1 5
~-
_ ~ _
i,,,.' ~ ~
- I <
a.
_
-
I,,,,,,,,,,,,,,,, I, ,
J 0.025 0.05 0.075 0.1 0.125 0.15
~ y
0.02
O01
n
.nn1
-0 02
.n~`
Ann
-0.05
.n no
.n no
x=0.20 0.03
0.02
0.01
o
-0.01
-0.02
4.03
~0.04
-0.05
-0.06
-0.07
-0.08
-0.09
0.1
0.07'
0.1
Fig. 21 (cont.~: velocity field contours of the axial velocity component and cross flow vectors.
ACKNOWLEDGEMENTS
This work was sponsored by the Italian "Ministero
delle Infrastrutture e dei Trasporti" through the
INSEAN Research Program 2000-2002, and by the
Office of Naval Research contract N00014-00-1-0344
under the administration of Dr. Patrick Purtell.
Special thanks to M. Palini, G. Bartoccioni, M. Sellini,
L. Benedetti and F. La Gala for their aid in the
preparation of the experimental set-ups and in
collecting data.
REFERENCES:
t1] A. OLIVIERI, F. PISTANI AND R. PENNA. 2000.
"Detailed measurements of wave-pattern and
nominal wake of a fast displacement ship
model". Advances in Fluid Mechanics III. [8]
t2] J.H. DUNCAN. 1981. "An experimental
investigation of breaking waves produced by a
towed hydrofoil". Proc. R. Soc. Lon. A 377,
33 1 -348.
t3] A. DI MASCIO, R. MUSCARI "A model for the
simulation of spilling breaking waves"
submitted to J. Ship Res
[4] A. COLAGROSSI, M. LANDRINI, M.P. TULIN,
"Numerical Studies of Wave Breaking
Compared to Experimental Observations". 4th
7
Numerical Towing Tank Symposium
(NuTTS), Hamburg 2001.
R.R. DONG, J. KATZ, T.T. HUANG. "On the
structure of Bow Waves on a Ship Model"
1997. J. Fluid Mech. 346: 77-1 15
A. IAFRATI, E.F. CAMPANA. "Direct numerical
simulation of free surface tension dominated
and non-dominated breaking waves" submitted
to 24th Symposium on Naval Hydrodynamics,
ONR, 2002.
[7] A. IAFRATI, A. OLIVIERI, F. PISTANI and E.F.
CAMPANA. "Numerical and experimental study
of the wave breaking generated by a
submerged hydrofoil " 23r~ Symposium on
Naval Hydrodynamics, Val de Reuil 2000.
A. OLIVIERI, F. PISTANI, G. AVANZINI, F.
STERN and R. PENNA "Towing Tank
Experiments of Resistance, Sinkage and Trim,
Boundary Layer, Wake and Free Surface Flow
around a naval combatant INSEAN 2340
Model" IIHR Report N°421, September 2001.
[91 H.W. COLEMAN, W.G. STEELE. 1 995.
"Engineering Application of Experimental
Uncertainty Analysis". AIAA J., Vol.33, N.10,
pp. 1888-1895.
OCR for page 303
[10] ITTC 1996 Report of the resistance and flow
committee. 21St International Towing Tank
Conference, Trohdheim.
[11] A. Olivieri, F. Pistani, R. Penna. 2002.
INSEAN Technical Report (in preparation).
[12] A. Di Mascio, R. Broglia and B. Favini 2001
"A second order goudunov-type scheme for
naval hydrodynamics", Godunov Methods,
Theory and Application, edited by E.F. Toro,
Kluwer Academic/Plenum Publishers,
[13] P. R. Spalart, S.R. Allmaras 1994 "One-
equation turbulence model for aerodynamic
flows", La Recherce Aerospatiale, Vol. 1, p. 5.
8
OCR for page 304
DISCUSSION
Luis Perez-Rojas
Polytechnical University of Madrid, Spain
The author presents some values for the
uncertainty analysis on the wave elevation
measurements. I would like to point out that in
these kind of measurements, each point has a
value for its uncertainty and in my opinion is not
correct to give a mean value for uncertainty
analysis 0 refer the error to highest value of wave
election. I would appreciate the opinion of the
author in this matter.
o
-0.05
-0.1
A
AUTHORS' REPLY
We agree with the opinion of the discusser. In
fact, we do not give a mean value of the
uncertainty in the wave field, but the uncertainty
on four pointwise measurements camed out
respectively in the non-breaking (1,2),
intermediate (3) and breaking (4) regions
(fig. Rib.
We show the uncertainty on the time-averaged
(indicated by "mean" in the paper) and rms value
of the wave elevation in these points.
Finally, we refer the uncertainty values of the
time-averaged wave elevation to its maximum
modulus because it is a non-zero representative
value of the measured wave field.
~ W~. ~
''I -
, , , ~
, , , , . , , , , , , , , , , , , , , , , 1
0 0.1 0.2 0.3
x
Fig R.1: analyzed points for wave elevation uncertainty assessment; iso-levels of h r m s are shown to
underlying the wave breaking intensity.
Representative terms from entire chapter:
wave breaking
